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Measurement noise 100 times lower than the quantum-projection limit using entangled atoms


Quantum metrology uses quantum entanglement—correlations in the properties of microscopic systems—to improve the statistical precision of physical measurements1. When measuring a signal, such as the phase shift of a light beam or an atomic state, a prominent limitation to achievable precision arises from the noise associated with the counting of uncorrelated probe particles. This noise, commonly referred to as shot noise or projection noise, gives rise to the standard quantum limit (SQL) to phase resolution. However, it can be mitigated down to the fundamental Heisenberg limit by entangling the probe particles. Despite considerable experimental progress in a variety of physical systems, a question that persists is whether these methods can achieve performance levels that compare favourably with optimized conventional (non-entangled) systems. Here we demonstrate an approach that achieves unprecedented levels of metrological improvement using half a million 87Rb atoms in their ‘clock’ states. The ensemble is 20.1 ± 0.3 decibels (100-fold) spin-squeezed via an optical-cavity-based measurement. We directly resolve small microwave-induced rotations 18.5 ± 0.3 decibels (70-fold) beyond the SQL. The single-shot phase resolution of 147 microradians achieved by the apparatus is better than that achieved by the best engineered cold atom sensors despite lower atom numbers2,3. We infer entanglement of more than 680 ± 35 particles in the atomic ensemble. Applications include atomic clocks4, inertial sensors5, and fundamental physics experiments such as tests of general relativity6 or searches for electron electric dipole moment7. To this end, we demonstrate an atomic clock measurement with a quantum enhancement of 10.5 ± 0.3 decibels (11-fold), limited by the phase noise of our microwave source.

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Figure 1: Overall setup.
Figure 2: Squeezing and metrology.
Figure 3: Measured spin-noise reduction and coherence.
Figure 4: Clock implementation.


  1. 1

    Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004)

    ADS  CAS  PubMed  Google Scholar 

  2. 2

    Guéna, J., Abgrall, M., Clairon, A. & Bize, S. Contributing to TAI with a secondary representation of the SI second. Metrologia 51, 108–120 (2014)

    ADS  Article  Google Scholar 

  3. 3

    Rocco, E. et al. Fluorescence detection at the atom shot noise limit for atom interferometry. New J. Phys. 16, 093046 (2014)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Bloom, B. J. et al. An optical lattice clock with accuracy and stability at the 10−18 level. Nature 506, 71–75 (2014)

    ADS  CAS  Article  Google Scholar 

  5. 5

    Geiger, R. et al. Detecting inertial effects with airborne matter-wave interferometry. Nature Commun . 2, 474 (2011)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Gaaloul, N. et al. Quantum tests of the equivalence principle with atom interferometry. Acta Astronaut. 67, 1059–1062 (2010)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Weiss, D. S., Fang, F. & Chen, J. Measuring the electric dipole moment of Cs and Rb in an optical lattice. Bull. Am. Phys. Soc. APR03, J1.008 (2003)

  8. 8

    Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Wineland, D. J., Bollinger, J. J., Itano, W. M. & Heinzen, D. J. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67–88 (1994)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Eberle, T. et al. Quantum enhancement of the zero-area Sagnac interferometer topology for gravitational wave detection. Phys. Rev. Lett. 104, 251102 (2010)

    ADS  Article  Google Scholar 

  11. 11

    Eichler, C., Salathe, Y., Mlynek, J., Schmidt, S. & Wallraff, A. Quantum-limited amplification and entanglement in coupled nonlinear resonators. Phys. Rev. Lett. 113, 110502 (2014)

    ADS  CAS  Article  Google Scholar 

  12. 12

    The LIGO Scientific Collaboration. A gravitational wave observatory operating beyond the quantum shot-noise limit. Nature Phys . 7, 962–965 (2011)

  13. 13

    Taylor, M. A. et al. Biological measurement beyond the quantum limit. Nature Photon . 7, 229–233 (2013)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Gross, C., Zibold, T., Nicklas, E., Esteve, J. & Oberthaler, M. K. Nonlinear atom interferometer surpasses classical precision limit. Nature 464, 1165–1169 (2010)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Riedel, M. F. et al. Atom-chip-based generation of entanglement for quantum metrology. Nature 464, 1170–1173 (2010)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Hamley, C. D., Gerving, C. S., Hoang, T. M., Bookjans, E. M. & Chapman, M. S. Spin-nematic squeezed vacuum in a quantum gas. Nature Phys . 8, 305–308 (2012)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Appel, J. et al. Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit. Proc. Natl Acad. Sci. USA 106, 10960–10965 (2009)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Takano, T., Fuyama, M., Namiki, R. & Takahashi, Y. Spin squeezing of a cold atomic ensemble with the nuclear spin of one-half. Phys. Rev. Lett. 102, 033601 (2009)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Schleier-Smith, M. H., Leroux, I. D. & Vuletic, V. States of an ensemble of two-level atoms with reduced quantum uncertainty. Phys. Rev. Lett. 104, 073604 (2010)

    ADS  Article  Google Scholar 

  20. 20

    Leroux, I. D., Schleier-Simith, M. H. & Vuletic, V. Implementation of cavity squeezing of a collective atomic spin. Phys. Rev. Lett. 104, 073602 (2010)

    ADS  Article  Google Scholar 

  21. 21

    Leroux, I. D., Schleier-Smith, M. H. & Vuletic, V. Orientation-dependent entanglement lifetime in a squeezed atomic clock. Phys. Rev. Lett. 104, 250801 (2010)

    ADS  Article  Google Scholar 

  22. 22

    Sewell, R. J., Koschorreck, M., Napolitano, M., Dubost, B. & Mitchell, M. W. Magnetic sensitivity beyond the projection noise limit by spin squeezing. Phys. Rev. Lett. 109, 253605 (2012)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Muessel, W., Strobel, H., Linnemann, D., Hume, D. B. & Oberthaler, M. K. Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates. Phys. Rev. Lett. 113, 103004 (2014)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Bohnet, J. G. et al. Reduced spin measurement back-action for a phase sensitivity ten times beyond the standard quantum limit. Nature Photon . 8, 731–736 (2014)

    ADS  CAS  Article  Google Scholar 

  25. 25

    Chen, Z., Bohnet, J. G., Weiner, J. M., Cox, K. C. & Thompson, J. K. Cavity-aided nondemolition measurements for atom counting and spin squeezing. Phys. Rev. A 89, 043837 (2014)

    ADS  Article  Google Scholar 

  26. 26

    Lee, J., Vrijsen, G., Teper, I., Hosten, O. & Kasevich, M. Many-atom–cavity QED system with homogeneous atom–cavity coupling. Opt. Lett. 39, 4005–4008 (2014)

    ADS  Article  Google Scholar 

  27. 27

    Sørensen, A. S. & Mølmer, K. Entanglement and extreme spin squeezing. Phys. Rev. Lett. 86, 4431–4434 (2001)

    ADS  Article  Google Scholar 

  28. 28

    Lücke, B. et al. Detecting multiparticle entanglement of Dicke states. Phys. Rev. Lett. 112, 155304 (2014)

    ADS  Article  Google Scholar 

  29. 29

    Biedermann, G. W. et al. Zero-dead-time operation of interleaved atomic clocks. Phys. Rev. Lett. 111, 170802 (2013)

    ADS  CAS  Article  Google Scholar 

  30. 30

    Borregaard, J. & Sørensen, A. S. Near-Heisenberg-limited atomic clocks in the presence of decoherence. Phys. Rev. Lett. 111, 090801 (2013)

    ADS  CAS  Article  Google Scholar 

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We thank I. Teper, G. Vrijsen and J. Lee for technical contributions to the experiment. This work was support by DTRA, an NSSEFF fellowship and the ONR.

Author information




O.H., N.J.E., R.K. and M.A.K. carried out the experiment, analysed the data, and prepared the manuscript.

Corresponding author

Correspondence to Mark A. Kasevich.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Inferred entanglement depths, quantifying multi-particle entanglement.

The inferred spin noise variance (y axis) and the mean-square Bloch vector lengths (x axis) are plotted for the 5 × 105 atom data set. Note that the probe power decreases from left to right. The x-axis values are conservatively chosen to be the most probable value of the measured Bloch vector length distributions (Fig. 2c). A state below an M-particle boundary (purple lines labelled with particle numbers) is guaranteed to contain at least groups of M particles whose quantum states are non-separable. The blue data set establishes a lower bound on entanglement depth taking into account the residual inhomogeneity in atom–cavity coupling. The red data set, for reference, shows what we would have obtained had we ignored the small inhomogeneity. The ellipses correspond to the 68% statistical confidence intervals on the quoted values. Jmax = N/2. The third data point in each set shows the largest metrological improvement.

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Hosten, O., Engelsen, N., Krishnakumar, R. et al. Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 529, 505–508 (2016).

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